What’s going on in this figure? How is there a missing square? To understand why, here’s a related puzzle. Calculate the shaded area in blue. As usual, watch the video for a solution. The missing square illusion explained Or keep reading. . . . . M I N D . Y O U R . D E C I S I O N S . P U Z Z L E . . . . Answer To The Missing Square Puzzle And Finding Shaded Areas (Pretty much all posts are transcribed quickly after I make the videos for them–please let me know if there are any typos/errors and I will correct them, thanks). The shaded area is adapted from Reddit AskMath. The height of the ..read more

About 3 years ago I did a “short” video and post on this very same puzzle. The problem is going viral again, so I have prepared a longer video. Today’s topic is The Moscow Puzzles problem 37: “A book costs $1 plus half its price. How much does it cost?” It is a simple puzzle, but it has confused many people on the internet. As usual, watch the video for a solution. As usual, watch the video for a solution. Simple puzzle that is confusing the internet Or keep reading. . . . . M I N D . Y O U R . D E C I S I O N S . P U Z Z L E . . . . Answer To Price Of A Book Puzzle (Pretty much all posts ar ..read more

I was emailed this very interesting puzzle. A party host says to two strangers Abby and Barry, “Each of you knows which day of the week you were born on, but not the day of the week the other was born on. But I can tell you that Barry was not born on Monday, and you were born one day apart (on consecutive days).” He then asks Abby and Barry alternately if either can deduce the day of the week the other person was born on. Abby: “No.” Barry: “No.” Abby: “No.” Barry: “No.” Abby: “No.” Barry: “Yes!” What day of the week was Abby born on? Can you deduce the day of the week for Barry? I did a searc ..read more

Problem 1 What is the area of the blue rectangle? Problem 2 What is the length of the chord? Thanks John, Kevin, and Salim! As usual, watch the video for a solution. 2 Nice Geometry Puzzles Or keep reading. . . . . M I N D . Y O U R . D E C I S I O N S . P U Z Z L E . . . . Answer To 2 Nice Geometry Puzzles (Pretty much all posts are transcribed quickly after I make the videos for them–please let me know if there are any typos/errors and I will correct them, thanks). Problem 1 This was a lot harder for me than it looked at first. I did some research and while I could not find the original ..read more

Lila’s age is the sum of the digits of her math teacher’s age. (Both have already had their birthdays this year.) In 5 years, Lila’s age will be the product of the digits of her math teacher’s age at that time. How old is Lila now? The teacher’s age is a two-digit number. As usual, watch the video for a solution. Sum And Product of Digits In Age Puzzle Or keep reading. . . . . M I N D . Y O U R . D E C I S I O N S . P U Z Z L E . . . . Answer To Sum And Product of Digits In Age Puzzle (Pretty much all posts are transcribed quickly after I make the videos for them–please let me know if there ..read more

Problem 1 Thanks Vladi for the suggestion! The tangent line to the semicircle has a length of 5 cm. What is the area of the rectangle? Problem 2 Thanks Alec for the suggestion! If the large square has an area of 25 cm2, what is the combined area of the small square and rectangle? As usual, watch the video for a solution. Can you solve these seemingly impossible problems? Or keep reading. . . . . M I N D . Y O U R . D E C I S I O N S . P U Z Z L E . . . . Answer To Two Seemingly Impossible Problems (Pretty much all posts are transcribed quickly after I make the videos for them–please let me ..read more

There are 9 boxes below. Solve by using each digit from 1 to 9 exactly once to fill the 9 boxes. Using a letter to represent a digit in each box, the puzzle is: ab * c = de + fg = hi As usual, watch the video for a solution. Put The Digits 1 to 9 In Boxes Puzzle Or keep reading. . . . . M I N D . Y O U R . D E C I S I O N S . P U Z Z L E . . . . Answer To Put The Digits 1 to 9 In Boxes Puzzle (Pretty much all posts are transcribed quickly after I make the videos for them–please let me know if there are any typos/errors and I will correct them, thanks). ab * c = de + fg = hi If b were equal ..read more

Problem 1 Thanks to Kanad from India for the suggestion! If f(x) = 4x/(4x + 2), then what is the value of: f(1/1997) + f(2/1997) + f(3/1997) + … + f(1996/1997) Problem 2 Simplify the product into the form a/b for integers a and b that are relatively prime. (1 – 1/22)(1 – 1/32)…(1 – 1/20232) As usual, watch the video for a solution. Two nice sums from India and Morocco Or keep reading. . . . . M I N D . Y O U R . D E C I S I O N S . P U Z Z L E . . . . Answer To Two Nice Sums From India And Morroco (Pretty much all posts are transcribed quickly after I make the videos for them–please let me k ..read more

Problem 1 A square is inscribed along the right angle of a right triangle, as shown, with vertical and horizontal lengths to the corners of 5 and 20. What is the area of the square? Problem 2 Thanks to Nifty for the suggestion! Four triangles are shown with dimensions: a, b, 6 area = 4 b, c, 6 area = 5 d, a, 6 area = 13 c, d, 6 area = ? Solve for the unknown area. As usual, watch the video for a solution. Can you solve for the area? Or keep reading. . . . . M I N D . Y O U R . D E C I S I O N S . P U Z Z L E . . . . Answer To Two Interesting Geometry Problems (Pretty much all posts are tra ..read more

These are a couple of puzzles from Puzzling StackExchange. Problem 1 Alice, Bob and Charlie are one of each type: a truth-teller (always tells truth), a liar (always lies) and a spy (can lie or tell the truth). Alice says she is not a truth-teller; Bob says he is not a spy; and Charlie says he is not a liar. What type is Charlie? A) Truth-teller B) Liar C) Spy D) There is not enough information Problem 2 Charlie has $1000. He can buy his favorite chocolate bar for $1. And there is a promotion: for every 4 chocolate wrappers submitted, the store will give 1 chocolate bar. What is the maximum nu ..read more